Spectral Asymptotics for Krein-Feller-Operators with respect to Random Recursive Cantor Measures

Abstract

We study the limit behavior of the Dirichlet and Neumann eigenvalue counting function of generalized second order differential operators $\frac{d}{d\mu }\frac{d}{dx}$, where $\mu$ is a finite atomless Borel measure on some compact interval $[a,b]$. We firstly recall the results of the spectral asymptotics for these operators received so far. Afterwards, we give the spectral asymptotics for so called random recursive Cantor measures. Finally, we compare the results for random recursive and random homogeneous Cantor measures.

References in corpus (2)

• Spectral Asymptotics for $V$-variable Sierpinski Gaskets
• Spectral Asymptotics for Krein-Feller-Operators with respect to $\mathbf{V}$-Variable Cantor Measures

Cited by in corpus (1)

• Spectral Asymptotics for Krein-Feller-Operators with respect to $\mathbf{V}$-Variable Cantor Measures